Dipole vector associated with charges

In summary, the conversation discusses a problem involving a dipole moment associated with two charges q1 and q2. The problem asks for the magnitude and direction of the dipole vector at point P, as well as the sum of the charges and the use of Coulomb's Law for electric field. It is determined that the dipole formulas may not work at close range and that parts (b) and (c) are misleading in relation to part (d).
  • #1
cookiemnstr510510
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Homework Statement


Problem attached in Dipole.Jpg

Homework Equations


The Attempt at a Solution


I am fine with Part A of the problem. I am just trying to understand what part B is asking. Are they asking what is the magnitude and direction of the dipole vector associated with charges q1 and q1 at point P? It is not clear to me. If so they would be asking about the dipole vector associated with the plane that bisects the dipole so I would use E(dipole)=-(1/4pi episolonnot) P/r^3? P is dipole moment
So really I would use -kqs/r^3 where s is distance between charges.
I can't imagine what else the problem is asking.
Another question would be is the q in the above equation the sum of q1 and q2?
Any help would be much appreciated!
Thanks in advanced!
 

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  • #2
I would avoid trying to solve this one with dipole formulas. The dipole formulas work for ## r>>d ##. I don't know that they work at close range. The simplest way to solve it is just to use vectors and the inverse square law.
 
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  • #3
They are asking for the dipole moment associated with the two charges. The dipole moment relative to a point is given by summing the charge multiplied by the position vector over all charges. For an overall neutral charge configuration, this does not depend on the point. The dipole moment is not the electric field.

Charles Link said:
I would avoid trying to solve this one with dipole formulas. The dipole formulas work for ## r>>d ##. I don't know that they work at close range. The simplest way to solve it is just to use vectors and the inverse square law.
You cannot solve B without using an expression for the dipole moment since the problem asks you to find the dipole moment. This part of the problem has nothing to do with the part of finding the field at p.
 
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  • #4
I was looking ahead to (d) which the OP seems to be referring to, by mentioning an electric field proportional to ## \frac{1}{r^3} ##. ## \\ ## (b) amd (c) are relatively simple, and I think it is misleading the student to try to get them to use these results to solve (d) in this problem.
 
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  • #5
The OP is asking about part B, not part D.

cookiemnstr510510 said:
Im just trying to understand what part B is asking.

The issue is understanding that the dipole moment is not the electric field, but what I described in #3.
 
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  • #6
cookiemnstr510510 said:

Homework Statement


Problem attached in Dipole.Jpg
dipole-jpg.jpg

Homework Equations



The Attempt at a Solution


I am fine with Part A of the problem. I am just trying to understand what part B is asking. Are they asking what is the magnitude and direction of the dipole vector associated with charges q1 and q1 at point P? It is not clear to me. If so they would be asking about the dipole vector associated with the plane that bisects the dipole so I would use E(dipole)=-(1/4pi episolonnot) P/r^3? P is dipole moment
So really I would use -kqs/r^3 where s is distance between charges.
I can't imagine what else the problem is asking.
Another question would be is the q in the above equation the sum of q1 and q2?
Any help would be much appreciated!
Thanks in advanced!
Part (b) asks a question about a dipole vector but says nothing about "at point P".
Part (c) also asks a question about a dipole vector..

Answer Parts (a) and (d) using Coulomb's Law, for electric field. These parts have nothing to do with dipoles.
 

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  • #8
Hmmm. I assume the dipole vector that is associated with the two charges in question (q1 &q2), will create an electric field at point P? I've attached my logic "dipole problem.JPG"
 

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  • #9
Charles Link said:
I was looking ahead to (d) which the OP seems to be referring to, by mentioning an electric field proportional to ## \frac{1}{r^3} ##. ## \\ ## (b) amd (c) are relatively simple, and I think it is misleading the student to try to get them to use these results to solve (d) in this problem.
Yes I believe I was mixing equations up from the book, my notes, and my head. I will look at D now and see if I can make sense of that one. Thanks!
 
  • #10
A detailed analysis of the dipole formulas show that they are intended for distances ## r>>d ## and will not work at close range. In this sense, in this combination of 4 questions, (b) and (c) are really unrelated and are misleading you. The results in (b) and (c) can not be used to solve part (d).
 
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  • #11
SammyS said:
View attachment 230535

Part (b) asks a question about a dipole vector but says nothing about "at point P".
Part (c) also asks a question about a dipole vector..

Answer Parts (a) and (d) using Coulomb's Law, for electric field. These parts have nothing to do with dipoles.
Ahh, okay. I guess that's true. So
cookiemnstr510510 said:
Hmmm. I assume the dipole vector that is associated with the two charges in question (q1 &q2), will create an electric field at point P? I've attached my logic "dipole problem.JPG"
Okay, Just read some responses. So this is not correct then. Ill go back and read on what Dipole Vector means.
 
  • #12
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  • #13
Charles Link said:
For the OP: All they are asking for in parts (b) and (c) is at the top part of this "link": http://hyperphysics.phy-astr.gsu.edu/hbase/electric/dipole.html
Thanks for the link. Is it true that the statement " what is the magnitude and and direction of the dipole vector" is referring to the dipole moment? and If so it would be
P=Qa(-i) ?
 
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  • #14
  • #15
To give you a quick introduction to it, the ## \frac{1}{r^3} ## behavior of electric and magnetic dipoles is actually very useful in analyzing some rather advanced E&M (electricity and magnetism) problems, and is used in the computation of the electric and/or magnetic fields at a distance from what are microscopic dipoles (with very small ## d ##). ## \\ ## In this problem, they are teaching you in parts (b) and (c) a couple of simple definitions, but nothing more than that. The ## \frac{1}{r^3} ## formulas do not apply at very close range=they do not give a correct result.
 
  • #16
cookiemnstr510510 said:
Thanks for the link. Is it true that the statement " what is the magnitude and and direction of the dipole vector" is referring to the dipole moment? and If so it would be
P=Qa(-i) ?
For part (b): Yes .
 
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  • #17
SammyS said:
For part (b): Yes .
Okay, therefore part C would be:
P=2Qa(i)
 
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  • #18
cookiemnstr510510 said:
Okay, therefore part C would be:
P=2Qa(i)
Yes.
 
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  • #19
Thanks everyone! appreciate the help :)
 
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1. What is a dipole vector associated with charges?

A dipole vector associated with charges is a vector that represents the separation between two opposite charges. It is a measure of the magnitude and direction of the electric dipole moment, which is the product of the charge and the distance between them.

2. How is the dipole vector calculated?

The dipole vector is calculated by taking the difference between the position vectors of the positive and negative charges. It can be represented mathematically as: p = q(r2 - r1), where p is the dipole vector, q is the charge, and r1 and r2 are the position vectors of the charges.

3. What is the significance of the dipole vector?

The dipole vector is significant because it helps to understand the behavior of electric charges and their interactions. It is also used to calculate the electric field strength at different points in space and can provide insight into the overall symmetry of a system.

4. Can the dipole vector change over time?

Yes, the dipole vector can change over time if the charges are moving or if the distance between them changes. This can occur in situations such as an alternating current circuit or when charged particles are accelerating.

5. How is the dipole vector related to the dipole moment?

The dipole vector is directly related to the dipole moment, as it is the physical representation of the dipole moment. The magnitude of the dipole moment is equal to the product of the charge and the distance between the charges, while the direction is determined by the direction of the dipole vector.

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